How to draw straight lines of a given length
Since all your measures are integers and all your angles are 45 degrees, you can use Precision control.

Once you have started an extrusion (E) the displacement is displayed at the bottom of the 3D Viewport:


(image from here)

Keeping an eye on it, before accepting the new position, you can hold down Ctrl (while moving the pointer) for "snapping" the transform to an integer number of grid units, or 10 grid units: it depends on your current zoom level. If you need a 10 times finer precision, hold Ctrl and Shift together.

For 45 degrees displacements, make sure that Dx and Dy are the same value, apart from the sign.

Once you have done, you can measure distances and angles using the MeasureIt addon.